Paul Blain Levy
p.b.levy at cs.bham.ac.uk
Fri Jan 8 20:17:34 EST 2021
I've just written the following paper and posted it at
(A slightly older version is on arXiv.)
Comments are welcome. Do you agree with me that Broad Infinity is an
intuitive axiom scheme?
Broad Infinity and Generation Principles
This paper introduces Broad Infinity, a new and arguably intuitive axiom
scheme. It states that ``broad numbers'', i.e.\ three-dimensional trees
whose growth is controlled, form a set. If the Axiom of Choice is
assumed, Broad Infinity is equivalent to the Ord-is-Mahlo scheme: every
closed unbounded class of ordinals contains a regular ordinal.
Whereas the axiom of Infinity leads to generation principles for
families, sets and ordinals, Broad Infinity leads to more advanced
versions of these principles. The paper relates these principles under
various prior assumptions: the Axiom of Choice, the Law of Excluded
Middle, and weaker assumptions.
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